Three-dimensional nonlinear H_2/H_∞ guidance law based upon approach of solving the state feedback Nash balance point

Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash balance point is mentioned. Upon this,a theorem about the solution of the state feedback control is given,the Lyapunov stabilization of the nonlinear system under this control is proved,too. At the same time,this solution is used to design the nonlinear H2/H∞ guidance law of the relative motion between the missile and the target in three-dimensional(3D) space. By solving two coupled Hamilton-Jacobi partial differential inequalities(HJPDI),a control with more robust stabilities and more robust performances is obtained. With different H∞ performance indexes,the correlative weighting factors of the control are analytically designed. At last,simulations under different robust performance indexes and under different initial conditions and under the cases of intercepting different maneuvering targets are carried out. All results indicate that the designed law is valid.

Athletes who train on unstable compared to stable surfaces exhibit unique postural control strategies in response to balance perturbations

Background:Athletes have been shown to exhibit better balance compared to non-athletes(NON).However,few studies have investigated how the surface on which athletes train affects the strategies adopted to maintain balance.Two distinct athlete groups who experience different types of sport-specific balance training are stable surface athletes(SSA) such as basketball players and those who train on unstable surfaces(USA) such as surfers.The purpose of this study was to investigate the effects of training surface on dynamic balance in athletes compared to NON.Methods:Eight NON,eight SSA,and eight USA performed five 20-s trials in each of five experimental conditions including a static condition and four dynamic conditions in which the support surface translated in the anteroposterior(AP) or mediolateral(ML) planes using positive or negative feedback paradigms.Approximate entropy(Ap En) and root mean square distance(RMS) of the center of pressure(Co P) were calculated for the AP and ML directions.Four 3 × 5(group × condition) repeated measures ANOVAs were used to determine significant effects of group and condition on variables of interest.Results:USA exhibited smaller Ap En values than SSA in the AP signals while no significant differences were observed in the ML Co P signals.Generally,the negative feedback conditions were associated with significantly greater RMS values than the positive feedback conditions.Conclusion:USA exhibit unique postural strategies compared to SSA.These unique strategies seemingly exhibit a direction-specific attribute and may be associated with divergent motor control strategies.

Microstructures and dynamic processes within the five-phase system:Regarding COVID-19 as a complex system

The research uses the development of 2019 novel coronavirus disease(COVID-19)in the human body as an example to explore the microstructures and dynamic processes of a concise complex system from the lens of the five-phase system.Based on the structural balance theory and system dynamics,the research finds that Iransitive triads and cyclic triads in the fivephase system are both imbalanced.The integration of these differentiated triads comprises of a balaneed intermediate form in the shape of quadrangular cycles.These cycles serve as microstructures of the five-phase system,due to the inherent balancing feedback mechanism,and support the generation of resultants.The alter nation of quadra ngular cycles drives the spirali ng development of the whole system.By orderly and regular in terweaving of sig ned directed links,the research provides a holistic,process-oriented demonstrati on for the developme nt processes of COVID-19.It clarifies that the esse nee of the five-phase system is phase-tra nsition processes with the quadrangular cycle as carrier and supporter,rather than the static aggregati on of five elements.The research deep ens the understanding of system non linearity by visualizi ng the circular causality and promotes the academic dialogue between the Western process theory and the Chinese inherited notion of the fivephase system.